8.3. Testing a Mean Hypothesis http://www.ck12.org
8.3 Testing a Mean Hypothesis
Learning Objectives
- Calculate the sample test statistic to evaluate a hypothesis about a population mean based on large samples.
- Differentiate the difference in hypothesis testing for situations with small populations and use the Student’s
t-distribution accordingly. - Understand the results of the hypothesis test and how the terms ’statistically significant’ and ’not statistically
significant’ apply to the results.
Introduction
In the previous sections, we have covered:
- the reasoning behind hypothesis testing.
- how to conduct single and two-tailed hypothesis tests.
- the potential errors associated with hypothesis testing.
- how to test hypotheses associated with population proportions.
In this section we will take a closer look at some examples that will give us a bit of practice in conducting these tests
and what these results really mean. In addition, we will also look at how the termsstatistically significantandnot
statistically significantapply to these results.
Also, it is important to look at what happens when we have a small sample size. All of the hypotheses that we have
examined thus far have assumed that we have normal distributions. But what happens when we have a small sample
size and are unsure if our distribution is normal or not? We use something called the Student’s t-distribution to take
small sample size into account.
Evaluating Hypotheses for Population Means using Large Samples
When testing a hypothesis for a normal distribution, we follow a series of four basic steps:
- State the null and alternative hypotheses.
- Set the criterion (critical values) for rejecting the null hypothesis.
- Compute the test statistic.
- Decide about the null hypothesis and interpret our results.
In Step 4, we can make one of two decisions regarding the null hypothesis.
- If the test statistic falls in the regions above or below the critical values (meaning that it is far from the mean),
we can reject the null hypothesis.